A tiling of the plane, $\mathcal{T}$, is a family of sets- called tiles- that cover the plane without gaps or overlaps. Assume that tiles are regular polygons and tiling is edge-to-edge.
A tiling is said to be periodic when there are two linearly independent translations for which the tiling is invariant.
I am studying about periodic tiling with regular polygons, but I do not know how to obtain two linearly independent translations in the periodic tiling?
I am so thankful if you help me or introduce a reference for it.